How do you solve algebraic equations?

The aim of solving an algebraic equation (such as x²=4(x-3)² ) is to find the values of x which make the equation correct. There are easy steps to follow for every question which can help you find the answer/s.expand all the terms in the equation, e.g. x² = 4(x-3)² x² = 4(x-3)(x-3) x² = 4(x² -6x +9) x² = 4x² - 24x +36move all the terms over to one side and simplify 0 = 4x² -24x +36 -x² 0 = 3x² -24x +36 --> 3, 24 and 36 are divisible by three 0 = x² - 8x +12factorise the terms 0=x² -8x +12 --> 8 is negative, 12 is positive, so the two factors must be negative 3x4 = 12, 6x2=12 3+4=7, 6+2=8 0=(x-6)(x-2)In order for this to be true, one of the terms must be equal to zero (either x-6 or x-2)Therefore:if x-6 =0 then x=6if x-2 =0 then x=2So x=6, x=2 are the two possible solutions. The equation is now solved